Cruithne is extraudinarily small and quite faint with distances that can have it further away than the sun from Earth so it isn't going to show any extended angular shape through a telescope and its faintness though less removed than resolving its 5 kilometer (approximately) size is still extreme. You would probably find Vesta and Ceres the asteroids more within reach.

Although 3753 Cruithne approaches Earth in November, I think it would be far too small and dim for any common backyard scope visually. I believe it was discovered photographically using a one meter scope (?).

If you haven't done so, you might want to search and ask around in the NEO and Solar System Observing forums. There are a number of knowledgeable asteroid observers on the forum.

Yes, Ceres certainly and Vesta with good luck. S&T used to publish finder charts in, I believe, January of each year. I no longer subscribe so I'm not sure if they still do. But I'm sure you can find good charts on the Net.

Well I guess it must be official that 3753 Cruithne is a satellite of Earth, if it’s being discussed in the Lunar Observing forum. Of course planetoid is an obsolete term that inappropriately employed the suffix “oid”. Cruithne is actually an asteroid or minor planet with an orbital period that averages one year in the long run. The Earth does appear to gravitationally keep it locked into that oscillating one year orbital period. During some eras it appears to loop around the Earth. But for centuries it can appear to oscillate opposite the Sun from the Earth, which makes it difficult to think of it as a satellite of Earth. I suppose the term quasi-satellite is worth consideration.

In this decade little Cruithne remains rather far from Earth and appears continuously outward from Earth’s morning side. It is currently at a distance of 0.616 AU and magnitude +17.0.

The brightest asteroids are 4 Vesta, 2 Pallas, 1 Ceres and 7 Iris. They are the only ones that ever get brighter than magnitude +7.0, unless we count rare NEO visitations. Coincidentally, both Vesta and Ceres will reach opposition and greatest brilliance for their current apparitions in December. Normally Vesta is noticeably brighter than Ceres, but during their upcoming oppositions Vesta will be near its aphelion and Ceres near its perihelion. Therefore Vesta will not appear much brighter than Ceres. For my asteroid apparition preview diagrams and graphs of the brightness of ten asteroids, visit my asteroid webpage at: www.CurtRenz.com/asteroids

Curt it is interesting how technology identifys our periodic interlopers like that. Who would have guessed it ever? I do want to make a concerted effort on Ceres. If I could l nab a pinch of something that'd make it different than a star of similar magnitude.